Polytopal realizations of non-crystallographic associahedra

TL;DR

This paper demonstrates that non-crystallographic associahedra can be realized as sections of simply-laced associahedra using a folding technique, extending the geometric understanding of these structures.

Contribution

It introduces a folding method to obtain non-crystallographic associahedra from simply-laced ones, broadening the geometric framework of generalized associahedra.

Findings

Non-crystallographic associahedra are sections of simply-laced associahedra.

Folding technique effectively constructs non-crystallographic associahedra.

Extends geometric realization methods to non-crystallographic root systems.

Abstract

We use the folding technique to show that generalized associahedra for non-simply-laced root systems (including non-crystallographic ones) can be obtained as sections of simply-laced generalized associahedra constructed by Bazier-Matte, Chapelier-Laget, Douville, Mousavand, Thomas and Yildirim.